Abstract
We consider a one-parametric family of conformal mappings from the upper half-plane onto the family of the polygons obtained by an angle-preserving shift of one or more vertices of some initial polygon. We obtain some differential equation for the family of mappings and some system of ordinary second-order differential equations for the preimages of the vertices of the family of polygons with Cauchy initial-value conditions.
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The authors were supported by the Russian Foundation for Basic Research (Grant 18–31–00190\( \backslash \)19).
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Kolesnikov, I.A., Sharofov, A.K. A One-Parametric Family of Conformal Mappings from the Half-Plane onto a Family of Polygons. Sib Math J 61, 818–829 (2020). https://doi.org/10.1134/S0037446620050055
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DOI: https://doi.org/10.1134/S0037446620050055